# 1911 Encyclopædia Britannica/Graphical Methods

**GRAPHICAL METHODS**, devices for representing by geometrical
figures the numerical data which result from the quantitative
investigation of phenomena. The simplest application is met
with in the representation of tabular data such as occur in
statistics. Such tables are usually of single entry, *i.e.* to a certain
value of one variable there corresponds one, and only one, value
of the other variable. To construct the graph, as it is called,
of such a table, Cartesian co-ordinates are usually employed.
Two lines or axes at right angles to each other are chosen, intersecting
at a point called the origin; the horizontal axis is the
axis of abscissae, the vertical one the axis of ordinates. Along
one, say the axis of abscissae, distances are taken from the origin
corresponding to the values of one of the variables; at these
points perpendiculars are erected, and along these ordinates
distances are taken corresponding to the related values of the
other variable. The curve drawn through these points is the
graph. A general inspection of the graph shows in bold relief
the essential characters of the table. For example, if the world's
production of corn over a number of years be plotted, a poor
yield is represented by a depression, a rich one by a peak, a.
uniform one over several years by a horizontal line and so on.
Moreover, such graphs permit a convenient comparison of two
or more different phenomena, and the curves render apparent
at first sight similarities or differences which can be made out from
the tables only after close examination. In making graphs for
comparison, the scales chosen must give a similar range of
variation, otherwise the correspondence may not be discerned.
For example, the scales adopted for the average consumption of
tea and sugar must be ounces for the former and pounds for the
latter. Cartesian graphs are almost always yielded by automatic
recording instruments, such as the barograph, meteorograph,
seismometer, &c. The method of polar co-ordinates is more
rarely used, being only specially applicable when one of the
variables is a direction or recorded as an angle. A simple case is
the representation of photometric data, *i.e.* the value of the
intensity of the light emitted in different directions from a
luminous source (see Lighting).

The geometrical solution of arithmetical and algebraical problems is usually termed graphical analysis; the application to problems in mechanics is treated in Mechanics, § 5, *Graphic Statics*, and Diagram. A special phase is presented in Vector Analysis.